28 Trans. Acad. Set. of St. Louis. 



o 



dr ' vR 



d 2 T T da 



(48) 



o 



di' 2 ' vR dr 



(49) 



The relation between density and temperature can be 

 deduced from the celebrated equation of Poisson, 



P IT, 

 P 



40 (50) 



which may be put in the form 



rp \2.44 



f-S" 



Substituting in (43) for a, ^r- and a their values given by 



equations (51), (49), and (48), we have 

 vR d 2 T 2>R dT 3<r„ / T 



2uR dT 3o (Ty« _ 

 + T n r -dr~ + R^[Tj ~ "' ( ^ 



T dr 2 



Putting t=, = ? and yp = ??, this equation may be written 



o 



^.+1*1^ (53) 



which is the form given by Ritter. We may determine 

 the three constants of this differential equation, as well as 

 the two constants of integration as follows. By the equation 



4 

 M = 7, toR?, the constant a is to betaken as known, when 

 o 



R and M are given, as we here assume; and the value r = R, 



c = 1, corresponds to a = 1, and by equation (48) 



dT _ T\_ dy 1_ 



dr vR ' dz v ' 



Thus the constant v is equivalent to the negative reciprocal 

 dr} 



value of tt for £ = 1. Moreover, T = 0, and ?? = 0, for 



